| 王选,祝雪峰,胡平,盖赟东.基于NURBS插值的三维渐进结构优化方法[J].计算力学学报,2016,33(4):536~542 |
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| 基于NURBS插值的三维渐进结构优化方法 |
| Bi-directional evolutionary method using NURBS interpolation for optimal design of 3D continuum structures |
| 投稿时间：2016-05-04 修订日期：2016-06-04 |
| DOI：10.7511/jslx201604018 |
| 中文关键词: 拓扑优化 等几何分析 双向渐进结构法 三维结构 NURBS |
| 英文关键词:topology optimization isogeometric analysis BESO method 3D structure NURBS |
| 基金项目:国家自然科学基金（11272075，11302041）；中央高校基本科研业务费专项（DUT15RC（4）36）资助项目. |
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| 中文摘要: |
| 提出一种基于等几何控制点密度变量的三维双向渐进结构拓扑优化方法。在当前列式下，高阶NURBS基函数被同时用于CAD模型中NURBS实体片的几何场、位移场和温度场以及密度场插值，实现了几何模型、分析模型和优化模型的有效统一，确保了位移场、温度场及密度场的高阶连续性；详细推导了基于等几何控制点密度变量的三维渐进结构法模型及其灵敏度分析列式；最后几个典型的数值算例，包括最小柔顺性、热传导优化问题及三维结构自由振动的基频最大化问题，验证了本文方法的有效性。 |
| 英文摘要: |
| A modified bi-directional evolutionary method utilizing the NURBS interpolation scheme with penalization is introduced for topology optimization of 3D continuum structures.In the present approach,the NURBS basis function is applied for the description of both the displacement field,temperature field and the geometry,as well as the interpolation of the element density field.Based on these,the design model and analysis model can be combined closely to realize the computational analysis directly on exact geometry.The model of BESO method using NURBS interpolation and its sensitivity analysis are detailed for three different optimization problems,that is the minimal mean compliance problem,steady heat conduction problem and frequency optimization problems.Numerical examples demonstrate the present formulation provides an effective means for topology optimization of 3D continuum structures. |
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